Penny Blood: Serial Sensation and Working-Class Entertainment — page 83: what you’re looking at

Machine-transcribed from the original scan — historical spelling and the odd misread are preserved.

66 ELEVATIONS ON THE for. v1. and for the smaller, a (Xz rat + = a'b x 11393 — 2EVa x 0-00468 | The general term of the series is ,o 1 (-1) < (n Gari) Garay" ( “ ==(~1)*abd re (z)"" 7 | (2%-+1) (2n+2) \a " Taking 2a as the superior limit of the integral, the general term becomes | (2n +1) (2n + 2) 1 Qan-+1 =(- Tad FF enti) (w+) 1 = geet =(-1)"ab 5 [n+12n+1° And putting n+1 for n the next term to this will be — 1 gants -(-1) \n+22n+3° And the sum of the two terms 2ietl ¢ 1 23 (—1)* ” intl +1 sie (2 +2) mrs Qeetl = 2n* — (n — 2) =(— 1)" ” in+2 (2n +1) (Qn+3) TITTLE rrr eee (A). Giving to » the series of values 0, 2, 4, 6, ..., 14, we obtain for the sum of the terms to the 16 inclusive, ab x 1°273320. Hence we have for the value of fPndx, when «= 2a (or at the superior limit), V2a — ab x 1:273320 ; 20 os o= | Pndz= V (2a — x) — ab x 1:273320 z bet det 11 at Tol2 73°4at |2 5 6a! 1 1 gets) erste qn +t; . | Ode= | ( | “Pnde) de=V (202 - =) ~ 1-273820aba Bild, 1d ie Li i ig a(23 3°4°6a% 25° 6° Tat ‘jl tI 1 tL gts yet FE et [m7 2n+12n+22n+3 qin +(-1)* +(- COLA @ NOOKS ACO